Abstract: This review article consists of two parts. In the first part we use theformalism of exceptional generalized geometry to derive the scalar fieldspace of SU2xSU2-structure compactifications. We show that in contrast toSU3xSU3 structures, there is no dynamical SU2xSU2 structureinterpolating between an SU2 structure and an identity structure.Furthermore, we derive the scalar manifold of the low-energy effective actionfor consistent Kaluza-Klein truncations as expected from N=4 supergravity.In the second part we then determine the general conditions for the existenceof stable Minkowski and AdS N=1 vacua in spontaneously broken gauged N=2supergravities and construct the general solution under the assumption that twoappropriate commuting isometries exist in the hypermultiplet sector.Furthermore, we derive the low-energy effective action below the scale ofpartial supersymmetry breaking and show that it satisfies the constraints ofN=1 supergravity. We then apply the discussion to special quaternionic-Kahlergeometries which appear in the low-energy limit of SU3xSU3-structurecompactifications and construct Killing vectors with the right properties.Finally we discuss the string theory realizations for these solutions.